混合最小化问题下重构块稀疏信号的充分条件
A Sufficient Condition on Recovery of Block Sparse Signals via Mixed Minimization
- 武汉大学学报（理学版）
- 作者机构：
1.宁波大学 数学与统计学院，浙江 宁波 315211
- 作者简介：
卜 京，男，硕士生，现从事积分变换与图像处理研究。E-mail：1216967781@qq.com
E-mail： wangjinping@nbu.edu.cn
- 基金信息：国家自然科学基金(62071262)
DOI：10.14188/j.1671-8836.2020.0248
中图分类号： O177.92纸质出版日期：2021-04-24，
收稿日期：2020-10-20，
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引用本文
卜京,王金平.混合最小化问题下重构块稀疏信号的充分条件[J].武汉大学学报（理学版）,2021,67(2):185-189.
BU Jing,WANG Jinping.A Sufficient Condition on Recovery of Block Sparse Signals via Mixed Minimization [J].J Wuhan Univ （Nat Sci Ed）,2021,67(2):185-189.
卜京,王金平.混合最小化问题下重构块稀疏信号的充分条件[J].武汉大学学报（理学版）,2021,67(2):185-189. DOI：10.14188/j.1671-8836.2020.0248
BU Jing,WANG Jinping.A Sufficient Condition on Recovery of Block Sparse Signals via Mixed Minimization [J].J Wuhan Univ （Nat Sci Ed）,2021,67(2):185-189. DOI：10.14188/j.1671-8836.2020.0248(Ch).
摘要
基于混合最小化问题，提出了测量矩阵的块鲁棒零空间特性（robust null space property，rNSP），在有噪声情况下证明rNSP是稳定重构块稀疏信号的充分条件。并且当块限制等距常数小于0.453 1时，证明块限制等距性蕴含着块鲁棒零空间特性。
Abstract
This paper focuses on the mixed minimization case and proposes the block robust null space property（rNSP） of measurement matrix, and then proves that the block rNSP is a sufficient condition to stably recover block sparse signals in noisy systems. Then we prove that the block restricted isometry property implies the block rNSP when block restricted isometry constant is less than 0.453 1.
关键词
块鲁棒零空间特性块限制等距性混合最小化块稀疏
Keywords
block robust null space propertyblock restricted isometry propertymixed minimizationblock sparse
references
HUO H Y， SUN W C， XIAO L. New conditions on stable recovery of weighted sparse signals via weighted http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294172&type=http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294169&type=2.032000063.04799986 minimization ［J］. Circuits， Systems， and Signal Processing， 2018， 37（7）： 2866-2883. DOI：10.1007/s00034-017-0691-6http://dx.doi.org/10.1007/s00034-017-0691-6.
ALDROUBI A， CHEN X M， POWELL A. Stability and robustness of http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294163&type=http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294176&type=2.032000063.04799986 minimization using null space property［EB/OL］. ［2020-06-30］. https：//www.researchgate.net/publication/267725837https://www.researchgate.net/publication/267725837.
WANG Y， WANG J J， XU Z B. Restricted http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294167&type=http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294165&type=1.523999932.96333337-isometry properties of nonconvex block-sparse compressed sensing［J］. Signal Processing， 2014， 104： 188-196. DOI：10.1016/j.sigpro.2014.03.040http://dx.doi.org/10.1016/j.sigpro.2014.03.040.
ELDAR Y C， MISHALI M. Robust recovery of signals from a structured union of subspaces［J］. IEEE Trans Inform Theory， 2009， 55： 5302-5316. DOI： 10.1109/TIT.2009.2030471http://dx.doi.org/10.1109/TIT.2009.2030471.
FOUCART S， LAI M J. Sparsest solutions of underdetermined linear systems via http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294182&type=http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294180&type=2.032000063.04799986 minimization for http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294214&type=http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294199&type=12.361333853.21733332［J］. Appl Comput Harmon Anal， 2009， 26：395-407.
WANG Y， WANG J J， XU Z B. On recovery of block-sparse signals via mixed http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294203&type=http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294201&type=20.912666323.97933340 norm minimization［J］. EURASIP Journal in Signal Processing， 2013， 76（1）：1-17. DOI：10.1186/1687-6180-2013-76http://dx.doi.org/10.1186/1687-6180-2013-76.
LIN J H， LI S. Block sparse recovery via mixed http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294208&type=http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294205&type=5.757333763.38666677 minimization［J］. Acta Mathematica Sinca（English Series）， 2013， 29（7）： 1401-1412. DOI：10.1007/s10114-013-1564-yhttp://dx.doi.org/10.1007/s10114-013-1564-y.
GAO Y， PENG J G， YUE S G. Stability and robustness of http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294212&type=http://html.publish.founderss.cn/rc-pub/api/common/picture?pictureId=46294210&type=5.672666553.38666677-minimization for block sparse recovery ［J］. Signal Processing， 2017， 137： 287-297. DOI：10.1016/j.sigpro.2017.02.012http://dx.doi.org/10.1016/j.sigpro.2017.02.012.
LAI M J， LIU L Y. A New Estimate of Restricted Isometry Constants for Sparse Solutions ［EB/OL］. ［2020-02-10］. http：//www.math.uga.edu/~mjlai/papers/LaiLiu11.pdfhttp://www.math.uga.edu/~mjlai/papers/LaiLiu11.pdf.
CANDÈS E J. The restricted isometry property and its implications for compressed sensing［J］. Comptes Rendus Mathematique，2008， 346（9/10）： 589-592. DOI：10.1016/j.crma.2008.03.014http://dx.doi.org/10.1016/j.crma.2008.03.014.
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